Their staff will be allowed to excavate a site on Rougier Street after several office blocks are demolished to make way for an aparthotel and restaurant development.
The area, near York Station, is close to the original Roman crossing of the River Ouse and will be the biggest archaeological dig to take place in York since the Viking project in Coppergate in the 1970s, which led to the opening of Jorvik Viking Centre.
The three buildings to be bulldozed include a bar, the Rougier House offices and Northern Rail's headquarters, Northern House.
Developers North Star have committed to opening a permanent visitor attraction at the site once a 145-bed hotel and 228 apartments are built to form a 'Roman Quarter'.
York Archaeological Trust have called the dig a 'once in a generation' opportunity.
Excavations will last for two years and gantries will be erected to allow the public to view the work.
York was known as Eboracum during the Roman period and was an important military base and administrative capital.
In 2011 the Trust completed extensive Roman excavations at the Hungate development site, which then became housing.
In April 2018, builders were stunned to discover sixty Roman skeletons buried beneath the swimming pool of a York hotel during renovation work. They were thought to have been interred in an extension to two Roman cemeteries that had already been studied nearby.